The quadrantal rule is not much good under the London TMA.
You realistically only have 900 safe feet to chose altitudes from, and in turbulent conditions you dont want to be using the last 300 ft of those.
In this area a radar service is desperately needed for GA. By that I mean one that will always be there, and as I have said in other threads, I fully appreciate the service Heathrow and Thames do give when they can.